Historically, enquiry into the size of the ultimate constituents of physical reality has been sharply divided into two : the ‘space’ size and the ‘time’ size, volume and duration. This is doubtless in part because we take our physics from the Greeks who were considerably more interested in space than in time : they were especially pre-eminent in sculpture, an art of space, and geometry which is, in the Euclidian version at any rate, quite literally ‘timeless’. At quite an early date the Greeks thinkers postulated that matter could be reduced to ‘four elements’ (Earth, Air, Fire and Water) and Thales guessed that Water was the most basic of all, a very remarkable idea since we now believe that hydrogen is the most abundant chemical element. Democritus of Abdera, followed by Epicurus and others, went further, arguing as early as the Vth century BC that there were ‘ultimate’ physical entities that he baptised ‘atoms’ and which were indivisible and eternal. The atomic theory was revivived at the Renaissance and led on to Newton’s Mechanics and Dalton’s ideas about the mixing of chemical substances. By the end of the nineteenth century, an early sketch of the interior of the atom, still regarded as indivisible, emerged.
During all this long period (2,500 years) there was little or no mention of time. Archimedes founded the science of statics but it was only some two thousand years later that Galileo (anticipated by Oresme) founded dynamics, the study of bodies in motion. No one in the West seems to have thought that there were any ultimate temporal intervals : Newton likened time to a river, i.e. to a fluid in continual motion. This involved Newton and others in certain difficulties since, in their dynamics, they found themselves obliged to attribute a series of exact positions to a continually moving particle and, moreover, to assume that a body subject to an applied force can be in accelerated motion during the whole of its trajectory, i.e. during any time interval however small. But the successful use of ‘infinitesimals’ in Calculus silenced most of the doubters (though not Bishop Berkeley who scented out at once the inherent illogicality of this proceeding).
Things were very different in India, a civilisation that seems to have been much more interested in time than in space. Buddhism is actually founded on the perception of transience and ‘deliverance’ depends on wholeheartedly accepting and welcoming this state of affairs instead of struggling against it. According to Stcherbatsky (Buddhist Logic), certain Indian Buddhist thinkers made a rough estimate of a fundamental ‘unit of time’ as early as the second century AD — though he does not give any details. More frequently though, Hinayana Buddhists speak of a dharma as having ‘zero duration’ on the principle that nothing at all can happen ‘within it’. Since everything is made up of dharma(s) this raises at once the difficulty of how there can be any duration to anything at all — which nonetheless there must be since it ‘takes a very long time’ indeed to attain nirvana.
In Western science, very belatedly, the idea of an ultimate unit of time,was apparently first advanced by Robert Lévi who baptised it by the name of chronon. Henry Margenau proposed that it be defined as radius electron/speed of light presumably on the principle that ‘nothing could happen’ faster than the speed of light and that there was nothing smaller than an electron (as it was then supposed). The radius of an electron is about 10 (exp –20) m, i.e. 1 /100000000000000000000 metres and the speed of light is about 3 × 10 (exp 8) metres per second. Clearly, Margenau’s ‘chronon’ is a very short interval of time — I make it around 3.3 /10(exp 29) secs.
Caldirola proposed a minimal time interval of 6.97 × 10 (exp –24) but the most popular value for a chronon seems to be the so-called Planck time which checks out at 5.39× 10 (exp –44) secs, i.e. about 6 divided by 1 followed by 44 noughts. These estimates of a minimum time interval are not taken out of a hat : Cadriola for example claims that such a value “allows for a clear answer to the question of whether a falling charged particle does or does not emit radiation” (Chronon, Wikipedia).
The New Scientist 9 July 2011 published an article by Anil Ananthaswamy entitled “How big is a grain of space-time?” which discusses the claim made by Laurent and his colleagues from Saclay, France, that the size of such a grain is around 10 (exp –48) metres. Rovelli and others objected that “a grain of space-time cannot be smaller than the Planck length”. (This value is for ‘size’ and not for the ‘time interval’ as such.)
It is certainly heartening that some scientists are at last beginning to question the continuous model of space-time which has reigned supreme for so long. Currently, investigations into the ‘ultimate’ nature of matter are leading us ever further away from the material into ghostlike regions : some string theories apparently even attribute ‘zero extension’ to their basic building blocks. But I am coming from the opposite direction. I start by assuming that the ultimate constituents of physical reality are not in any sense ‘objects’ but are ‘ultimate events’, the equivalent of the Hindu Buddhists’ dharma, and that everything is discontinuous (with the possible exception of the Event Locality itself). From this position I want to see if anything useful can be deduced and/or what further assumptions are needed to gradually build up the more familiar ‘universe’ in which (we think) we live. The actual size of an ‘ultimate event’, or rather the size of the locus it occupies, will hopefully eventually emerge from experiment and deductions therefrom much as the size of molecules and atoms arose from ever more accurate measurements and observations on them. For the moment I am satisfied in my own mind that ultimate events really exist and occupy specific positions on an Event Locality. S.H.